Responses of Dynamic Systems Excited by Non‐Gaussian Pulse Processes

Abstract

This paper presents an efficient method for calculating the response statistics of dynamic systems subjected to Poisson‐distributed (non‐Gaussian) pulse processes. The procedure to be followed is based on an extension of the traditional method of the Itô stochastic differential equation, in which the increment of the Wiener process associated with the Itô stochastic differential equation has been substituted by the increment of a compound Poisson process. One major achievement here is the derivation of a general moment equation suitable to Poisson‐distributed pulse excitations. Two examples of application (for linear and nonlinear systems) are given to illustrate the use of the derived moment equation. Exact response moments for linear systems can be calculated efficiently. In studying a nonlinear oscillator with a use of fourth‐order cumulant‐neglect method, it is found that the calculation for response moments of second order is reasonably accurate, although this is not so for moments of fourth order.